What exactly do Threstrals have that makes them dangerous? Claws, teeth, size, any other magical abilities? We have a question asking IF they are dangerous, but I want to know what exactly they can use to hurt you or other creatures.
Actually, I'd like to clarify some confusion. Seems all Thestrals get a generic undeserved rap, over a few more dangerous ones.
According to Fantastic Beasts, winged horses aren't uniformly dangerous, and aren't all the same in general:
M.O.M. Classification: XX–XXXX Winged horses exist worldwide. There are many different breeds, including the Abraxan (immensely powerful giant palominos), the Aethonan (chestnut, popular in Britain and Ireland), the Granian (grey and particularly fast) and the rare Thestral (black, possessed of the power of invisibility, and considered unlucky by many wizards). As with the Hippogriff, the owner of a winged horse is required to perform a Disillusionment Charm upon it at regular intervals (see Introduction).
Not that some are far less dangerous (XX), but the giant Abraxans are (imagine a flying giant horse - even if it has a good temperament, you're at great risk)
Please note that while they are "predators", they aren't exactly man-eaters:
'Hmm,' said Professor Grubbly-Plank, her pipe waggling slightly as she talked. 'Looks like something's attacked her. Can't think what would have done it, though. Thestrals will sometimes go for birds, of course, but Hagrid's got the Hogwarts Thestrals well-trained not to touch owls.' (OOTP)
So unless you're an owl or other small bird, normal Thestrals aren't that more dangerous than any horse.
- Having said that, any farmer can tell you that a horse can be bloody dangerous. If it kicks you with back legs.... damage. Magical invisible flying horse is still a horse capable of kicking.
However, Abraxans are far larger (GoF calls them "elephantine") and at first glance, seem to not be too well-tempered:
The front three rows of students drew backwards as the carriage hurtled ever lower, coming in to land at a tremendous speed – then, with an almighty crash that made Neville jump backwards onto a Slytherin fifth-year's foot – the horses' hooves, larger than dinner plates, hit the ground. A second later, the carriage landed too, bouncing upon its vast wheels, while the golden horses tossed their enormous heads and rolled large, fiery red eyes. (GoF)
'My steeds require – er – forceful 'andling,' said Madame Maxime, looking as though she doubted whether any Care of Magical Creatures teacher at Hogwarts could be up to the job. 'Zey are very strong –'(GoF)
Imagine a flying elephant/buffalo, with mean temper, and carnivorous. I can see why that'd get XXXXX - you'd get hurt from simply handling the large animal as Madame Maxine says; or if they attack you they squish you; or they can bite you far worse than bird-eating regular ones. Or a kick from one would be even more deadly (imagine elephant kick or stomp).
Although Thestrals seem to generally be fairly placid, any animal can be dangerous in the right circumstances.
If you've ticked one off, according to Hagrid the biggest thing you have to worry about is probably their teeth:
"Are you aware," Umbridge said loudly, interrupting him, “that the Ministry of Magic has classified Thestrals as 'dangerous'?"
Harry's heart sank like a stone, but Hagrid merely chuckled.
"Thestrals aren' dangerous! All righ', they might take a bite outta yeh if yeh really annoy them -"
Order of the Phoenix Chapter 21: "The Eye of the Snake"
Being carnivorous scavengers, their teeth are certainly rather sharp; they're seen ripping the flesh off a cow carcass:
A pair of blank, white, shining eyes were growing larger through the gloom and a moment later the dragonish face, neck and then skeletal body of a great, black, winged horse emerged from the darkness. It surveyed the class for a few seconds, swishing its long black tail, then bowed its head and began to tear flesh from the dead cow with its pointed fangs.
Hagrid pointed at the cow carcass on the ground. The whole class stared at it for a few seconds, then several people gasped and Parvati squealed. Harry understood why: bits of flesh stripping themselves away from the bones and vanishing into thin air had to look very odd indeed.
Order of the Phoenix Chapter 21: "The Eye of the Snake"
Beyond that, they're basically just winged horses. I wouldn't want to get too close to their back legs if I caught one in a bad mood, and it's not clear what they can do with their wings (but I suspect it would rather hurt), but there doesn't seem to be any other major dangers.
According to the Harry Potter wiki, Thestrals are carnivores and while they contain powerful magic, it doesn't seem they have any additional powers other than their invisibility to people who have not experienced death.
To quote the above page:
They are very rare, and are considered dangerous by the Ministry of Magic. Thestrals are, undeservedly, known as omens of misfortune and aggression by many wizards because they are visible only to those who have witnessed death at least once (and fully accepted the concept) or due to their somewhat grim, gaunt and ghostly appearance.
It seems that they are mostly feared because of their appearance, and because they are large, powerful, fast creatures that can fly and is attracted to the scent of blood. There is no mention of sharp fangs or claws, but given they are carnivores then they must have formidable weapons such as these to allow them to overpower their prey. There seems to be no canon about having any other magical abilities that I can find.
So are they dangerous? Well, a large flying carnivore that is invisible to anyone who has not experienced death would probably be quite dangerous.